Solve for $x$ : $4x^2 + 48x + 128 = 0$
Answer: Dividing both sides by $4$ gives: $ x^2 + {12}x + {32} = 0 $ The coefficient on the $x$ term is $12$ and the constant term is $32$ , so we need to find two numbers that add up to $12$ and multiply to $32$ The two numbers $4$ and $8$ satisfy both conditions: $ {4} + {8} = {12} $ $ {4} \times {8} = {32} $ $(x + {4}) (x + {8}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 4) (x + 8) = 0$ $x + 4 = 0$ or $x + 8 = 0$ Thus, $x = -4$ and $x = -8$ are the solutions.